A financial market with interacting investors: does an equilibrium exist?

Christoph Frei*, Gonçalo dos Reis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

While trading on a financial market, the agents we consider take the performance of their peers into account. By maximizing individual utility subject to investment constraints, the agents may ruin each other even unintentionally so that no equilibrium can exist. However, when the agents are willing to waive little expected utility, an approximated equilibrium can be established. The study of the associated backward stochastic differential equation (BSDE) reveals the mathematical reason for the absence of an equilibrium. Presenting an illustrative counterexample, we explain why such multidimensional quadratic BSDEs may not have solutions despite bounded terminal conditions and in contrast to the one-dimensional case.

Original languageEnglish
Pages (from-to)161-182
Number of pages22
JournalMathematics and Financial Economics
Volume4
Issue number3
Early online date26 Feb 2011
DOIs
Publication statusPublished - 30 Apr 2011

Keywords / Materials (for Non-textual outputs)

  • Approximated equilibrium
  • Interacting investors
  • Multidimensional BSDE
  • Quadratic generator
  • Relative performance

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